UNION CITY — Hoping to avert further erosion of district services because of state budget cuts, the New Haven school board has hired consultants to determine the likelihood that voters would support a parcel tax to fund school programs.

But board members are split over whether to ask voters for money when families increasingly are strapped for cash.

One trustee, who supported further consideration of a tax, implied that the timing is not ideal. Just last November, voters agreed to tax themselves $3.2 million annually for eight years to pay for public-safety services.

Nevertheless, school board President Gertrude Gregorio said, “We cannot wait for Sacramento to give us adequate funding. … I know this is not the best time to ask our community for more money, but … if the budget continues the way it is, there’s no way we can afford to give our children (what we want). It’s an expensive proposition, but it’s needed.”

In a 3-2 vote, with trustees Michelle Matthews and Gwen Estes dissenting, the board on Tuesday approved hiring two consulting groups for a maximum of $54,500 to conduct initial assessments to determine voter interest in a tax. Any decision to place a tax measure on a ballot would require another board vote.

At this point, Superintendent Kari McVeigh said, “What we’re really trying to find out is, ‘Will this community support any parcel tax, and if so, under what terms and how much?'”‰”

The Center for Community Opinion, one of the consulting groups, will survey 400 registered voters by phone next month, according to a tentative schedule proposed to the district. Board members suggested that at least one community forum be held in addition to the phone surveys to ensure that every community member has an opportunity to weigh in.

Another firm, Hahn and Associates, will act as political consultants and help craft messages to the public about the need for a tax.

Last spring, the school board slashed $7 million. This year, it’s made $4 million in budgetary adjustments through cuts and borrowing money from itself, and has approved $5.9 million more in cuts from the 2009-10 and 2010-11 budgets.

With the reductions, the district plans to increase class sizes, stop offering co-curricular activities, eliminate its busing program and possibly close an elementary school in the next two years.

New Haven is not the only district to consider turning to voters for additional revenue.

The Fremont school board recently directed its superintendent to meet with consultants to discuss a similar parcel tax and is scheduled to receive an update next week. Newark officials also have mentioned the idea of a tax measure.